Simplify (2 square root of -2)(3 square root of 4)

$(2 \sqrt{- 2}) (3 \sqrt{4})$

Rewrite $- 2$ as $- 1 (2)$ .

$2 \sqrt{- 1 (2)} (3 \sqrt{4})$

Rewrite $\sqrt{- 1 (2)}$ as $\sqrt{- 1} \cdot \sqrt{2}$ .

$2 (\sqrt{- 1} \cdot \sqrt{2}) (3 \sqrt{4})$

Rewrite $\sqrt{- 1}$ as $i$ .

$2 (i \cdot \sqrt{2}) (3 \sqrt{4})$

Rewrite $4$ as $2^{2}$ .

$2 i \sqrt{2} (3 \sqrt{2^{2}})$

Pull terms out from under the radical, assuming positive real numbers.

$2 i \sqrt{2} (3 \cdot 2)$

Multiply $3$ by $2$ .

$2 i \sqrt{2} \cdot 6$

Multiply $6$ by $2$ .

$12 i \sqrt{2}$